Barber of Seville - hilarious. Or Don Giovanni - which is the first opera I ever saw and was so mesmerised by the performance that on coming away afterwards I drove down a one way street the wrong way only to enocounter a police car driving towards me! For me Madame Butterfly would not be a good idea as it has too much recit - so difficult to understand what's going on.

I agree with Laurie O'Brien: Everything with Christopher Maltman would be perfect - perhaps his Papageno in April is a good suggestion for beginners.
Otherwise I think L'elisir d'amore, La Traviata, Rigoletto, La Boheme, Tosca or Barber of Seville are a good idea. In my opinion Figaro and Cosi are extremely boring (too much recit), but in the end it depends: you can never know what's the right opera to fix a special person. One of my friends fell in love with opera after a Salome.

I will never forget the first time I went to La Scala performing La Gioconda di Ponchielli. Great the combinations of Opera and dance, with music familiar and easy to listen to, dinamic and emotional.
Another one could be Il Viaggio a Reims di Rossini, ideal to introduce Opera to a beginner, allegra and exiting.

I once introduced a group of my young piano students to opera with a video of La Boheme by the Australian Opera. They were enthralled and talked about it for years afterwards.
For newcomers I would also recommend L'Elisir d'Amore. Rolando Villazon is my tenor of choice in the role of Nemorino - delightfully portrayed with just the right mix of sensitivity and humour.

We saw our first opera in March 2013 and picked Tosca because it was playing on my wife's birthday. All I can say is wow! We were totally bowled over. We were told Tosca was a hard opera but we found it wonderful :)